Reliability estimation of k-unit series system based on progressiverly censored data


Abstract


In this article, we consider a k-unit series system with component lifetime distribution to be a member of the scale family of distributions. We discuss estimation of the scale parameter and estimation of reliability function of the family based on progressively Type-II censored sample. The maximum likelihood estimator (MLE) of the scale parameter is derived using Expectation-Maximization (EM) algorithm and is used to estimate reliability function. Confidence intervals are constructed using asymptotic distribution of MLE. β-expectation tolerance interval for lifetime of the system is obtained. We consider half-logistic distribution as a member of the scale family and study performance of the MLE, reliability estimate and confidence interval using simulation experiments.

DOI Code: 10.1285/i20705948v7n2p228

Keywords: Progressively Type-II censoring, EM algorithm, MLE, confidence interval, coverage probability, reliability, β-expectation tolerance interval, half-logistic distribution.

References


A. C. Cohen, Progressively censored samples in life testing, Technometrics, 5(1963), pp. 327-329.

N. R. Mann, Exact three-order-statistic confidence bounds on reliable life for a Weibull model with progressive censoring, J. Am. Stat. Assoc. 64 (1969), pp. 306-315.

N. R. Mann, Best linear invariant estimation for Weibull parameters under progressive censoring, Technometrics, 13 (1971), pp. 521-533.

N. Balakrishnan and A. Asgharzadeh, Inference for the Scaled Half-Logistic Distribution based on progressively Type-II censored samples, Commun. Stat. Theory and Methods, 34 (2005), pp. 73-87.

N. Balakrishnan, N. Kannan, C. T. Lin and H. K. T. Ng, Point and interval estimation for Gaussian distribution, based on Progressively Type-II Censored samples, IEEE Trans. Reliab. 52(1) (2003), pp. 90-95. (2)

N. Balakrishnan, N. Kannan, C. T. Lin and S. J. S. Wu, Inference for the extreme value distribution under Progressive Type-II Censoring, J. Statist. Comput. Simul. 74 (2004), pp. 25-45.

H. K. T. Ng, Parameter estimation for a modified Weibull distribution, for progressively Type-II censored samples, IEEE trans. Reliab. 54 (2005), pp. 374-380.

N. Balakrishnan and R. Aggarwala, Progressive Censoring: Theory, Methods and Applications, Birkhauser, Boston (2000).

N. Balakrishnan, Progressive Censoring Methodology: An Appraisal. Test, 16(2) (2007), pp. 211-259.

B. Pradhan, Point and Interval Estimation for the Lifetime Distribution of a k-Unit Parallel System Based on Progressively Type-II Censored Data, Eco. Qual. Control, 22, 2 (2007), pp.175-186.

C. Kim and K. Han, Estimation of the Scale Parameter of the Half-Logistic Distribution under progressively Type-II censored sample, Statist. Papers, 51(2010), pp. 375-387.

G. Iliopoulous, and N. Balakrishnan, Exact Likelihood Inference for Laplace Distribution based on Type-II censored samples, J. Statist. Plann. Inference, 141 (2011), pp. 1224-1239.

A. Asgharzadeh and R.Valiollahi, Estimation of the scale parameter of the Lomax distribution under progressive censoring, International Journal of Statistics and Economics, 6 (2011) pp. 37-48.

H. Krishna and M. Malik, Reliability estimation in Maxwell distribution with progressively Type-II censored data, J. Statist. Comput. Simul. 82 (2012), pp. 623-641.

H. Krishna and K. Kumar, Reliability estimation in Lindley distribution with progressively Type-II right censored data, Mathematics and Computers in Simulation, 82 (2011), pp.281-294.

H. Krishna and K. Kumar, Reliability estimation in generalized inverted exponential distribution with progressively Type-II censored data, J. Statist. Comput. Simul., Online published – http://dx.doi.org/10.1080/00949655.2011.647027.

Potdar K. G. and Shirke D. T., Inference for the scale parameter of lifetime distribution of k-unit parallelsystem based on progressively censored data, J. Statist. Comput. Simul., Online published– http://dx.doi.org/10.1080/00949655.2012. 700314.

Potdar K. G. and Shirke D. T., Inference for the distribution of a k-unit parallel system with exponential distribution as the component life distribution based on Type-II progressively censored sample, Int.J. Agricult. Stat. Sci., 8(2), pp.503-517.

A. P. Dempster, N. M. Laird and D. B. Rubin, Maximum Likelihood from Incomplete Data via the EM algorithm, J. R. Statist. Soc., B, 39(1977), pp. 1-38.

G. J. Mclachlan and T. Krishnan, The EM Algorithm and Extensions, John Wiley and sons, New York (1997).

R. J. A. Little and D. B. Rubin, Statistical analysis with missing data, John Wiley and sons, New York (2002).

B. Pradhan and D. Kundu, On Progressively Censored Generalized Exponential Distribution, Test, 18 (2009), pp.497-515.

H. K. T. Ng, P.S. Chan and N. Balakrishnan, Estimation of parameters from progressively censored data using EM algorithm, Comp. Statist. Data Analy., 39 (2002), 371-386.

T.A.Louis, Finding the observed information matrix using the EM algorithm, J. R. Statist. Soc., B, 44 (1982), pp.226-233.

R. R. Kumbhar and D. T. Shirke, Tolerance limits for lifetime distribution of k-Unit parallel system, J. Statist. Comput. Simul. 74 (2004), pp. 201-213.

W. Q. Meeker and L.A. Escober, Statistical Methods for Reliability Data, John Wiley & Sons, New York (1998.).

C. L. Atwood, Approximate tolerance intervals based on maximum likelihood estimator, J. Am. Stat. Assoc. 79 (1984), pp. 459-465.

N. Balakrishnan and R. A. Sandhu, A simple simulation algorithm for generating progressive Type-II censored samples, Am. Stat. 49 (1995), pp. 229-230.


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